Is it too hot to explore Naples & Mt Vesuvius in mid June?
That depends on your own comfort level, certainly lots of people manage to do it throughout the summer months.
If that is when you can visit then I wouldn't be concerned as much with the heat.
I've been to the area at that time or just before - some days were hot, but it wasn't unbearable. The average is 26 - 28 degrees Celsius (78 to 82 F) for mid June. I also went up Vesuvius, it was a hot day where water was essential, but it's not a difficult climb at all if you're reasonably fit even in hot weather.